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Article

Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms

1
Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology, Yokohama 226-8502, Japan
2
Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8502, Japan
3
Sony Computer Science Laboratories, Tokyo 141-0022, Japan
4
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
*
Author to whom correspondence should be addressed.
Academic Editor: Pentti Nieminen
Entropy 2021, 23(2), 168; https://doi.org/10.3390/e23020168
Received: 6 January 2021 / Accepted: 25 January 2021 / Published: 29 January 2021
(This article belongs to the Section Multidisciplinary Applications)
Although the sizes of business firms have been a subject of intensive research, the definition of a “size” of a firm remains unclear. In this study, we empirically characterize in detail the scaling relations between size measures of business firms, analyzing them based on allometric scaling. Using a large dataset of Japanese firms that tracked approximately one million firms annually for two decades (1994–2015), we examined up to the trivariate relations between corporate size measures: annual sales, capital stock, total assets, and numbers of employees and trading partners. The data were examined using a multivariate generalization of a previously proposed method for analyzing bivariate scalings. We found that relations between measures other than the capital stock are marked by allometric scaling relations. Power–law exponents for scalings and distributions of multiple firm size measures were mostly robust throughout the years but had fluctuations that appeared to correlate with national economic conditions. We established theoretical relations between the exponents. We expect these results to allow direct estimation of the effects of using alternative size measures of business firms in regression analyses, to facilitate the modeling of firms, and to enhance the current theoretical understanding of complex systems. View Full-Text
Keywords: business firms; companies; econophysics; multivariate scaling; nontrivial power–law exponents; size measures business firms; companies; econophysics; multivariate scaling; nontrivial power–law exponents; size measures
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MDPI and ACS Style

Kobayashi, Y.; Takayasu, H.; Havlin, S.; Takayasu, M. Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms. Entropy 2021, 23, 168. https://doi.org/10.3390/e23020168

AMA Style

Kobayashi Y, Takayasu H, Havlin S, Takayasu M. Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms. Entropy. 2021; 23(2):168. https://doi.org/10.3390/e23020168

Chicago/Turabian Style

Kobayashi, Yuh, Hideki Takayasu, Shlomo Havlin, and Misako Takayasu. 2021. "Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms" Entropy 23, no. 2: 168. https://doi.org/10.3390/e23020168

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